flopping a set vs top pair

[soko]

say sombody raises in NL, what odds are you looking at for them to hit top pair and you hit a set

ie. 55vsAK flopping a5x

[ohnonotthat]

Assuming you are certain the raisor has overcards (and NOT an overpair) the flop will produce a set for you AND top pair for him 2.775% of the time.

There are 2 cards that will give you a set; one (and only one) must appear.

There are 6 cards that will give him top pair; one (and only one) must appear.

The odd card must come be one of the 40 cards that will help neither him nor you.

2 x 6 x 40 = 480

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There are 17,296 possible flops . . . (48 x 47 x 46) / 3!

So . . .

These two events will both occur 480 times in 17,296 - or - 1 time in 36.033

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There are other methods for doing this type of calculation but I've always thought this was the easiest to understand (and explain).

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Note that this does not account for you flopping quads (or a full house); nor does it account for him flopping more than one pair.

I mention this only to be precise - these moonshot flops will occur very infrequently.